Isabelle Gallagher
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View article: The Cauchy problem for quasi-linear parabolic systems revisited
The Cauchy problem for quasi-linear parabolic systems revisited Open
We study a class of parabolic quasilinear systems, in which the diffusion matrix is not uniformly elliptic, but satisfies the Petrovskii condition (positivity of eigenvalues’ real part). Local well-posedness is known since the work of Aman…
View article: Low carbohydrate and low-calorie diets reduce liver fat and lower brain glutamate and myo-inositol levels in patients with Metabolic Dysfunction-Associated Steatotic Liver Disease (MASLD)
Low carbohydrate and low-calorie diets reduce liver fat and lower brain glutamate and myo-inositol levels in patients with Metabolic Dysfunction-Associated Steatotic Liver Disease (MASLD) Open
In a longitudinal cohort study with intervention (NCT05216796), we utilized multiorgan imaging to determine if metabolic dysfunction-associated steatotic liver disease (MASLD) is associated with elevated cerebral glutamate and myo-inositol…
View article: Striatal dopamine tone is positively associated with adiposity in humans as determined by PET using dual dopamine type-2 receptor antagonist tracers
Striatal dopamine tone is positively associated with adiposity in humans as determined by PET using dual dopamine type-2 receptor antagonist tracers Open
View article: Dietary Saturated Fat Intake Moderates the Effect of Plasma Triglycerides on Memory Performance in Middle-Aged Adults
Dietary Saturated Fat Intake Moderates the Effect of Plasma Triglycerides on Memory Performance in Middle-Aged Adults Open
View article: Brainstem Volume and White Matter Characteristics Associated with Cognitive Performance in Healthy Middle‐aged Adults
Brainstem Volume and White Matter Characteristics Associated with Cognitive Performance in Healthy Middle‐aged Adults Open
Background Traditionally linked to essential physiological functions, the brainstem is now acknowledged for its role in cognition and dementia. Abnormal tau protein accumulation starts in the brainstem. Late life brainstem volume at baseli…
View article: Structural and functional sex differences in medial temporal lobe subregions at midlife
Structural and functional sex differences in medial temporal lobe subregions at midlife Open
View article: Interplay of Large Neutral Amino Acids, Metabolic Syndrome, and Apolipoprotein E ε4 on Brain Integrity at Midlife
Interplay of Large Neutral Amino Acids, Metabolic Syndrome, and Apolipoprotein E ε4 on Brain Integrity at Midlife Open
Introduction: Large neutral amino acids (LNAAs) tryptophan and phenylalanine have been implicated in the pathogenesis of neurodegenerative diseases. Given limited research on the effects of LNAA on brain health across different life stages…
View article: Brain dopamine responses to ultra-processed milkshakes are highly variable and not significantly related to adiposity in humans
Brain dopamine responses to ultra-processed milkshakes are highly variable and not significantly related to adiposity in humans Open
Ultra-processed foods high in fat and sugar may be addictive, in part, due to their purported ability to induce an exaggerated postingestive brain dopamine response akin to drugs of abuse. Using standard [ 11 C]raclopride positron emission…
View article: Association between Large Neutral Amino Acids and Brain Integrity in Middle-Aged Adults at Metabolic Risk
Association between Large Neutral Amino Acids and Brain Integrity in Middle-Aged Adults at Metabolic Risk Open
This investigation delves into the interplay between large neutral amino acids (LNAA) and metabolic syndrome (MetS) in midlife adults, examining their collective influence on brain structure and cognitive function. While LNAA, such as tryp…
View article: Large Neutral Amino Acids Moderate the Effects of Metabolic Syndrome on Cognitive Performance in Middle-Aged Adults
Large Neutral Amino Acids Moderate the Effects of Metabolic Syndrome on Cognitive Performance in Middle-Aged Adults Open
Introduction: Two large neutral amino acids (LNAA), tryptophan and tyrosine, are precursors to cerebral neurotransmitters and are involved in cognitive function. Higher levels of LNAA in young adults are associated with impro…
View article: Dynamics of dilute gases: a statistical approach
Dynamics of dilute gases: a statistical approach Open
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View article: A linear stochastic model of turbulent cascades and fractional fields
A linear stochastic model of turbulent cascades and fractional fields Open
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular an…
View article: Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations
Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations Open
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square ro…
View article: Spectral summability for the quartic oscillator with applications to the Engel group
Spectral summability for the quartic oscillator with applications to the Engel group Open
In this article, we investigate spectral properties of the sublaplacian -\Delta_{G} on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approach to the Fourier analysis on the Engel group in terms of…
View article: Striatal dopamine tone is positively associated with body mass index in humans as determined by PET using dual dopamine type-2 receptor antagonist tracers
Striatal dopamine tone is positively associated with body mass index in humans as determined by PET using dual dopamine type-2 receptor antagonist tracers Open
The relationship between adiposity and dopamine type-2 receptor binding potential (D2BP) in the human brain has been repeatedly studied for >20 years with highly discrepant results, likely due to variable methodologies and differing study …
View article: Long‐time correlations for a hard‐sphere gas at equilibrium
Long‐time correlations for a hard‐sphere gas at equilibrium Open
It has been known since Lanford that the dynamics of a hard‐sphere gas is described in the low density limit by the Boltzmann equation, at least for short times. The classical strategy of proof fails for longer times, even close to equilib…
View article: Dietary fat restriction affects brain reward regions in a randomized crossover trial
Dietary fat restriction affects brain reward regions in a randomized crossover trial Open
BACKGROUNDWeight-loss diets often target dietary fat or carbohydrates, macronutrients that are sensed via distinct gut-brain pathways and differentially affect peripheral hormones and metabolism. However, the effects of such diet changes o…
View article: On the dynamics of dilute gases
On the dynamics of dilute gases Open
The evolution of a gas can be described by different mathematical models depending on the scale of observation. A natural question, raised by Hilbert in his sixth problem, is whether these models provide mutually consistent predictions. In…
View article: Dynamics of Dilute Gases at Equilibrium: From the Atomistic Description to Fluctuating Hydrodynamics
Dynamics of Dilute Gases at Equilibrium: From the Atomistic Description to Fluctuating Hydrodynamics Open
View article: Dynamics of dilute gases at equilibrium: from the atomistic description to fluctuating hydrodynamics
Dynamics of dilute gases at equilibrium: from the atomistic description to fluctuating hydrodynamics Open
We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon previous results of the authors where the asymptotics of the covariance of the fluctuation fie…
View article: Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group
Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group Open
It was proved by H. Bahouri, P. G{\\'e}rard and C.-J. Xu in [9] that the\nSchr{\\"o}dinger equation on the Heisenberg group $\\mathbb{H}^d$, involving the\nsublaplacian, is an example of a totally non-dispersive evolution equation: for\nth…
View article: Cluster expansion for a dilute hard sphere gas dynamics
Cluster expansion for a dilute hard sphere gas dynamics Open
In a previous paper by the authors, a cluster expansion method had been developed to study the fluctuations of the hard sphere dynamics around the Boltzmann equation. This method provides a precise control on the exponential moments of the…
View article: Spectral summability for the quartic oscillator with applications to the Engel group
Spectral summability for the quartic oscillator with applications to the Engel group Open
In this article, we investigate spectral properties of the sublaplacian $-Δ_{G}$ on the Engel group, which is the main example of a Carnot group of step 3. We develop a new approach to the Fourier analysis on the Engel group in terms of a …
View article: Restriction of dietary fat, but not carbohydrate, affects brain reward regions in adults with obesity
Restriction of dietary fat, but not carbohydrate, affects brain reward regions in adults with obesity Open
Weight loss diets often target restriction of dietary fat or carbohydrate, macronutrients that are sensed via distinct gut-brain pathways and differentially affect peripheral hormones and metabolism. However, the effects of such diet chang…
View article: Large, global solutions to the three-dimensional the navier-stokes equations without vertical viscosity
Large, global solutions to the three-dimensional the navier-stokes equations without vertical viscosity Open
The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main fe…
View article: Dynamics of dilute gases: a statistical approach
Dynamics of dilute gases: a statistical approach Open
The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…
View article: Dynamics of dilute gases: a statistical approach
Dynamics of dilute gases: a statistical approach Open
The evolution of a gas can be described by different models depending on the\nobservation scale. A natural question, raised by Hilbert in his sixth problem,\nis whether these models provide consistent predictions. In particular, for\nraref…
View article: Long-time derivation at equilibrium of the fluctuating Boltzmann\n equation
Long-time derivation at equilibrium of the fluctuating Boltzmann\n equation Open
We study a hard sphere gas at equilibrium, and prove that in the low density\nlimit, the fluctuations converge to a Gaussian process governed by the\nfluctuating Boltzmann equation. This result holds for arbitrarily long times.\nThe method…
View article: Strichartz Estimates and Fourier Restriction Theorems on the Heisenberg Group
Strichartz Estimates and Fourier Restriction Theorems on the Heisenberg Group Open
View article: Local dispersive and Strichartz estimates for the Schr{ö}dinger operator on the Heisenberg group
Local dispersive and Strichartz estimates for the Schr{ö}dinger operator on the Heisenberg group Open
It was proved by H. Bahouri, P. G{é}rard and C.-J. Xu in [9] that the Schr{ö}dinger equation on the Heisenberg group $\mathbb{H}^d$, involving the sublaplacian, is an example of a totally non-dispersive evolution equation: for this reason …